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Data compression and harmonic analysis

Publication ,  Journal Article
Donoho, DL; Vetterli, M; Devore, RA; Daubechies, I
Published in: IEEE Transactions on Information Theory
December 1, 1998

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transformbased image compression have been inspired by this result. In this paper we also discuss connections perhaps less familiar to the Information Theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were not obviously related to practical data compression, and have used a language not immediately accessible to outsiders. Nevertheless, through an extensive generalization of what Shannon called the "sampling theorem," harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations. We explain why harmonic analysis has interacted with data compression, and we describe some interesting recent ideas in the field that may affect data compression in the future. © 1998 IEEE.

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Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

December 1, 1998

Volume

44

Issue

6

Start / End Page

2435 / 2476

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

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Donoho, D. L., Vetterli, M., Devore, R. A., & Daubechies, I. (1998). Data compression and harmonic analysis. IEEE Transactions on Information Theory, 44(6), 2435–2476. https://doi.org/10.1109/18.720544
Donoho, D. L., M. Vetterli, R. A. Devore, and I. Daubechies. “Data compression and harmonic analysis.” IEEE Transactions on Information Theory 44, no. 6 (December 1, 1998): 2435–76. https://doi.org/10.1109/18.720544.
Donoho DL, Vetterli M, Devore RA, Daubechies I. Data compression and harmonic analysis. IEEE Transactions on Information Theory. 1998 Dec 1;44(6):2435–76.
Donoho, D. L., et al. “Data compression and harmonic analysis.” IEEE Transactions on Information Theory, vol. 44, no. 6, Dec. 1998, pp. 2435–76. Scopus, doi:10.1109/18.720544.
Donoho DL, Vetterli M, Devore RA, Daubechies I. Data compression and harmonic analysis. IEEE Transactions on Information Theory. 1998 Dec 1;44(6):2435–2476.

Published In

IEEE Transactions on Information Theory

DOI

ISSN

0018-9448

Publication Date

December 1, 1998

Volume

44

Issue

6

Start / End Page

2435 / 2476

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing